The Same Negation, the Opposite Inference: Logical Underdetermination in the Catuskoti as a Second Test of the Inferential Gap

Gaudapada's Mandukya Karika 4.22 and Nagarjuna's MMK 1:1 deploy formally identical four-fold negation of origination — both refute arising from self, other, both, and neither — yet derive maximally opposed metaphysical conclusions: ajativada ('There is an Unborn' — consciousness/Brahman as the non-originated substratum) versus sunyata ('There is no birth' — all things lack inherent existence, including any proposed substratum). The inferential gap between them can be localized to a single operation: whether the four-fold negation functions as paryudasa (implicative negation, where denying all modes of origination licenses the positive conclusion that something unoriginated must exist) or as prasajya-pratisedha (non-implicative negation, where denying all modes of origination merely establishes that origination is incoherent, without licensing any positive metaphysical claim). The formal syntax of the negation is identical in both cases. What differs is the semantic type assigned to the negation — and this assignment cannot be derived from the logical structure alone. It depends on a prior ontological commitment: Gaudapada assumes consciousness is self-evidently real and uses the argument to characterize it (it must be unoriginated); Nagarjuna assumes no entity can be established as ultimately real and uses the argument to demonstrate universal emptiness. This constitutes a second, sharper test of the inferential gap model because the underdetermination operates not on experiential data (which might be theory-laden) but on logical argument (whose formal structure is transparently identical across both thinkers). Combined with the first test (phenomenological underdetermination in objectless awareness) and the second (formal underdetermination in predictive processing), this establishes the inferential gap as a three-level invariant: it appears wherever a procedure (experiential, formal, or logical) eliminates all determinate content and forces the question of what, if anything, remains. The gap is not an accident of Indian intellectual history but a structural feature of any sufficiently rigorous negation procedure applied to the question of ultimate existence.

The scholarly debate about Gaudapada and Nagarjuna focuses primarily on historical questions (did Gaudapada borrow Buddhist dialectical techniques? is he a crypto-Buddhist?) or doctrinal questions (which conclusion is philosophically correct?). The present model reframes the relationship as a case of logical underdetermination — the four-fold negation itself is structurally neutral between the two conclusions, and the decisive factor is the type of negation (implicative vs. non-implicative) which cannot be read off from the formal syntax. This is analogous to the Duhem-Quine thesis in philosophy of science: the same experimental result underdetermines theory choice because auxiliary assumptions do the real work. Here, the same logical argument underdetermines metaphysical conclusions because the semantic type of negation (paryudasa vs. prasajya-pratisedha) does the real work — and this type-assignment is the philosophical commitment, not a consequence of the argument. The 'crypto-Buddhist' controversy about Gaudapada dissolves once you recognize that sharing a logical tool does not entail sharing a conclusion, because the tool is inference-neutral. Additionally, establishing the inferential gap as a three-level invariant (phenomenological, formal, logical) is new: it suggests the atman/anatta-type dispute is not resolvable by moving to a different register of argument (from experience to logic, or from logic to formal models) because the underdetermination persists at every level. This represents a structural impossibility result for comparative philosophy: no single framework can adjudicate between traditions that diverge at the level of what negation means.

Three serious objections challenge this model. (1) The logical forms may not actually be identical. Nagarjuna's catuskoti is embedded in a system of prasanga (consequentialist reductio) where the goal is to show that the opponent's own position collapses on its own terms — he is not advancing a thesis at all (MMK 29 and Vigrahavyavartani: 'I have no thesis'). Gaudapada IS advancing a thesis (ajativada as characterization of Brahman). If one argument is thesis-advancing and the other is thesis-denying, calling them 'formally identical' may be an artifact of extracting them from their dialectical contexts. The 'same logical structure' may be an illusion produced by decontextualization. (2) The distinction between paryudasa and prasajya-pratisedha may be a post-hoc rationalization rather than something operative in the original texts. Gaudapada does not explicitly flag his negation as implicative; later Advaitins (especially Suresvara) developed this distinction. Nagarjuna does not explicitly use the term prasajya-pratisedha — it is imposed by commentators (Candrakirti, Bhavaviveka). If the negation-type distinction is a commentarial overlay rather than an authorial intention, the model attributes philosophical precision that neither original author possessed. (3) Underdetermination may be trivially true. Any argument that concludes with a negation ('nothing arises') is compatible with any positive metaphysics that can incorporate that negation. Saying that formal logic underdetermines metaphysical conclusions may be no more illuminating than saying that 'it is raining' is compatible with both 'God made it rain' and 'atmospheric conditions caused it.' The model's explanatory power depends on whether the underdetermination is genuinely surprising or merely a restatement of the truism that logic alone cannot settle ontology.